In one of the stories that make up Garth Greenwell’s new book, the unnamed narrator and his boyfriend, R, visit a small gallery while on holiday in Bologna. They tour the rooms, full of “quiet and unambitious” art. At first the narrator is underwhelmed. Then, in front of one painting, something changes.

I liked the seeming naivety of it, the way the simple figures had been simplified further, purified or idealised to geometrical forms, almost, but rendered bluntly, imperfectly. And the brushstrokes were imperfect too, visible, haphazard, the paint distributed unevenly, inexpertly; but that wasn’t right, really it was striving for something ideal, that was what I felt, the frequency I wanted to catch.

With its doublings back (that “almost” and “but that wasn’t right”) and doublings down – a confidence fused with hesitancy – the passage is typical of Greenwell’s style. His writing is precise and fastidious, but it often describes unfinished or contingent thoughts, as though ideas were forever rehearsing themselves within his sentences. Here there’s a sense in which the narrator’s own striving – for the articulation of a vision, or a feeling to fit his thesis – is at least as important as what he’s looking at.

Cleanness revisits the places and some of the characters of Greenwell’s celebrated 2016 novel What Belongs to You (itself an expanded version of Mitko, his 2011 novella). It is set in Sofia, sometime around 2013, but really, apart from the odd reference to the internet, it could be any year. Not quite a novel, it is nonetheless a tightly structured book, eschewing chronological order in favour of a careful symmetry in which each story, apart from the central one, is mirrored by its thematic opposite.

The hinge of the book is an account of the relationship between the narrator, an American schoolteacher and aspiring writer living in Bulgaria (Greenwell himself worked as a teacher in Sofia for some years), and R, a closeted Portuguese student, there on an Erasmus exchange programme. Initially the narrator finds satisfaction in monogamy, the “commonness” of which makes him feel “some stubborn strangeness in me ease, I felt like part of the human race”. But after R returns to Lisbon, he begins to seek more extreme sexual experiences. He enjoys the physicality of sex, but another impulse is self-destruction. “It was a childish feeling, maybe,” he muses on returning to his old life of casual hookups. “I wanted to ruin what he had made, what he had made me, I mean, the person he had made me.”

Greenwell has spoken about the way gay sex can create private spaces amid public ones: the cruising spots in a city in which sexual activity goes on under the noses of straight society. His prose is like that too, at once inviting you in and holding you at arm’s length. The combination of intimacy and distance that characterises his writing is echoed in descriptions of sexual encounters, often with strangers, in which the line between desire and fear is so fine as to be invisible.

In one of the most compelling stories, “Gospodar” (which was first published in 2014), the narrator goes to a stranger’s flat for a BDSM session. Things go wrong, and become uncomfortable, then frightening. The scene has the urgency of a thriller, the rhythms mirroring the rising tension of the encounter. Greenwell charts clear-sightedly the delicate balance between wilful will-lessness and true powerlessness, which is for the narrator the main attraction of the experience. “Who knows why we take pleasure in such things,” he asks himself afterwards, “it’s best not to look into it too closely.”

Greenwell was a poet before he became a novelist, and the namelessness of the characters gives Cleanness the feel of a lyric poem, at once confessional and anonymous. The anonymity creates a space for biographical speculation, leaving you wondering whether you’re reading journal entries rather than fiction, and exactly whose propriety is being protected by those blank initials. But the ambiguity and lack of characterisation creates a problem too. Because everything is channelled through the mind of a single narrator, the book becomes, at times, overwhelmingly solipsistic.

In What Belongs to You the self-consciously writerly register of the first-person narrative seemed entirely appropriate to a character who had read plenty of Thomas Mann and WG Sebald and was escaping an abusive childhood to reinvent himself in a foreign land. In Cleanness the voice comes to feel fussy. Booksellers in a square display “their wares piled high under awnings” (“wares” being one of those words you only seem to come across in novels). During sex the narrator feels “a flood of extraordinary pleasure … a lifting and lightness and unsteadiness, as with certain drugs”. That “certain drugs” is typical: both pedantically specific and indistinct. What drugs?

In another story the narrator, after hearing that R wants to end their relationship, travels to a coastal town with a group of other writers for a workshop:

I was eager to be festive with these people, to distract myself from the grief I felt since receiving R’s message, my own grief and grief at the thought of him alone in his room in Lisbon – though I didn’t know where he was, of course, he had sent his message hours before and might already have recovered from his spasm of regret, who could know.

Here the diction (“be festive with”; “grief” instead of “sadness”) is mannered, while the clarifications (“of course”, “who could know”) feel performed rather than addressed to actual readers. If these are thoughts, they are thoughts that are begging to be overheard: it’s as though a serious and slightly pretentious gap-year student was writing earnestly in his journal after a disappointing night out.

In the preface to What Maisie Knew Henry James, whose influence can be felt so strongly in Greenwell’s sentences, wrote: “Small children have many more perceptions than they have terms to translate them; their vision is at any moment much richer, their apprehension even constantly stronger than their prompt, their at all producible, vocabulary.” The irony generated by that novel comes from us knowing more about the situation in which Maisie finds herself than she is able to articulate: we read the codes of the world she inhabits more fluently than she can. In Cleanness the effect is almost the opposite: the narrator has more words than he has perceptions or ideas, and the world he moves through appears far simpler than he wants it to be.

Fantasy, unconscious desire, the roles we are forced to perform by love: on all this, Cleanness is wise and illuminating, and Greenwell is clearly a talented writer of beautiful sentences, and an insightful guide to the strange ways people have of loving each other. But despite some astonishing and unsettling moments, this is a profoundly humourless book. Need sex always be so portentous? Need life?

• Cleanness is published by Picador (RRP £14.99).